Electric Quadrupole Hyperfine Constants Research Articles

Variation of the Quadrupole Hyperfine Structure and Nuclear Radius due to an Interaction with Scalar and Axion Dark Matter.

Atomic spectroscopy is used to search for the space-time variation of fundamental constants which may be due to an interaction with scalar and pseudoscalar (axion) dark matter. In this Letter, we study the effects that are produced by the variation of the nuclear radius and electric quadrupole moment. The sensitivity of the electric quadrupole hyperfine structure to both the variation of the quark mass and the effects of dark matter exceeds that of the magnetic hyperfine structure by 1-2 orders of magnitude. Therefore, the measurement of the variation of the ratio of the electric quadrupole and magnetic dipole hyperfine constants is proposed. The sensitivity of the optical clock transitions in the Yb^{+} ion to the variation of the nuclear radius allows us to extract, from experimental data, limits on the variation of the hadron and quark masses, the QCD parameter θ and the interaction with axion dark matter.

Theoretical analysis of the relativistic hyperfine interaction in 131Xe I

The relativistic hyperfine constants of the heavy inert gas element xenon-131 isotope have been calculated. The calculations, executed through the Multiconfiguration Dirac-Hartree-Fock method, yield the hyperfine constants of 128 levels belonging to the ns[K]J (n = 6, 7, 8, 9), nf [K]J (n = 4, 5, 6), nd[K]J (n = 5, 6, 7, 8), np[K]J (n = 6, 7, 8) and 5g[K]J intermediate Rydberg series. In order to draw further insights into the precision of our calculations and the accuracy of the obtained data, the resulting magnetic dipole and electric quadrupole hyperfine constants are analysed by comparing them with other experimental and theoretical results available in the atomic spectra database. Indeed, a satisfactory agreement is observed between our results and the other experimental and theoretical ones. Moreover, the absence of the hyperfine anomaly enables us to highlight the plausibility of our theoretical results through the calculation of the ratio A129A131 for a given state. The obtained values are found to be compatible with the ratio of nuclear moments of 129Xe and 131Xe isotopes. The consistency of these two different analyses confirms the accuracy of our data, on the one hand and classifies them as a reference in identifying the experimental spectrum in xenon, on the other hand. Based on this accuracy, the calculated values of the hyperfine constants for the levels under consideration, accompanied by the experimental values of the nuclear magnetic dipole and electric quadrupole moments, facilitated the calculation of the mean value of the magnetic as well as the electric field gradients produced by the electron at the tiny nucleus.

Extensive and accurate relativistic calculations of atomic data on the 83Kr I spectrum

We provide an extensive, accurate and complete new spectroscopic data set for many levels belonging to the intermediate perturbing Rydberg series ns[K]J (5 ≤ n ≤ 8), nd[K]J (4 ≤ n ≤ 7) and the autoionizing Rydberg series np[K]J (5 ≤ n ≤ 7) and nf[K]J (4 ≤ n ≤ 5) relative to the ground state 4p6 1S0 for neutral krypton-83 isotope. The data set is composed of the energy levels, the oscillator strengths the radiative transition rates the Landé g-factors, the magnetic dipole and electric quadrupole hyperfine constants. The values of these spectroscopic parameters are calculated in the multiconfiguration Dirac-Hartree–Fock (MCDHF) framework. The calculations are carried out in the active space where the electron correlation effects, contributions from relativistic configuration interaction (RCI), the quantum electrodynamics (QED) effects with transverse photon Breit interaction and vacuum photon polarization, specific mass shift and self-energy corrections are included. In addition, we provide the oscillator strengths and transition rates in Coulomb and Babushkin gauges for the 4p5(2P)4d–4p5(2P)5p, 4p5(2P)5s–4p5(2P)5p, 4p5(2P)6s–4p5(2P)5p, 4p5(2P)4d–4p5(2P)44f, 4p5(2P)5d–4p5(2P)4f, 4p5(2P)5d–4p5(2P)6p, 4p5(2P)7s–4p5(2P)6p, 4p5(2P)4d–4p5(2P)5f, 4p5(2P)5d–4p5(2P)5f, 4p5(2P)6d–4p5(2P)5f, 4p5(2P)7p–4p5(2P)6d and 4p5(2P)8s–4p5(2P)7p transition arrays. Extensive comparisons with other experimental and theoretical data from the reference databases are carried out in order to judge the reliability of our data. These comparisons indicate that our results are accurate. The present spectroscopic data may be useful for line identification in observed spectra as well as modelling and diagnostics of astrophysical and fusion plasmas.

Revised energy levels of singly ionized lanthanum

Based on the experimental wavenumbers of 344 spectral lines from calibrated Fourier transform (FT) spectra as well as wavenumbers of 81 lines from the wavelength tables from literature, the energy of 115 fine structure levels of singly ionized lanthanum has been revised by weighted global fits. The classifications of the lines are provided by numerous previous investigations of lanthanum by different spectroscopic methods and authors. For the high accurate determination of the center of gravity wavenumbers from the experimental spectrum, the hyperfine constants of the involved levels have been taken into account, if possible. For the 94 levels with known hyperfine constants the accuracy of energy values is better than 0.01 cm−1. For 34 levels the magnetic dipole hyperfine constants A have been determined from FT spectra as part of this work. For four of these 34 levels even electric quadrupole hyperfine constants B could be estimated. For levels, which have experimentally unknown hyperfine constants and which are connected only by lines not found in the FT spectra but taken from literature, the uncertainties of energy values are about a factor of 10 higher. A list of all revised level energies together with a compilation of hyperfine structure data is given as well as a list of all lines used.

Magnetic dipole and electric quadrupole hyperfine constants for V II 3d4, 3d3 4s and 3d2 4s2J = 1–5 states

Relativistic configuration interaction (RCI) calculations have been done for hyperfine constants and Lande g-values for 69 even parity V II states. Our results are in good agreement with the few recent experimental magnetic dipole results. We suggest that several Lande g-values need to be re-measured. Our electric quadrupole constants seem to be the first ones available. Analysis and methodology improvements include the introduction of an approximate sum rule for hyperfine constants, and a way of producing a more diagonal reference basis function set. The importance of mixing of 3dn−1 4s basis members with near degenerate 3dn or 3dn−2 4s2 is emphasized.

Collinear two-color saturation spectroscopy in CN A–X (1–0) and (2–0) bands

Hyperfine-resolved saturation spectra were measured for a selection of low and medium J rotational lines in the A2Π–X2Σ+ system of CN using two copropagating laser beams tuned to transitions in the (2–0) and (1–0) bands. A bleach laser was amplitude modulated and fixed in frequency near the center of a rotational line of the (2–0) vibrational band, while a probe laser was frequency-modulated and scanned across selected lines of the (1–0) vibrational band, sharing a common lower state with the bleach laser. Locking the probe laser with a tunable radio frequency offset to a cavity that tracks the slowly drifting bleach laser greatly improved the quality of the double-resonance saturation signals, by stabilizing the relative frequency of the two beams. The sub-Doppler resonances were fit with Lorentzian line shapes having a typical full-width at half maximum of 2–3MHz. The hyperfine spectra observed depend on the hyperfine structure within both rovibronic transitions excited, permitting the determination of hyperfine molecular constants in the υ=2 state and the refinement of previously published values in the υ=1 state. Four nuclear magnetic dipole and two electric quadrupole hyperfine constants were determined for each of the upper states from a fit with a weighted root mean squared error of 0.5MHz. The vibrational dependence of these constants is weak or negligible.

Hyperfine structure of laser-cooling transitions in fermionic erbium-167

We have measured and analyzed the hyperfine structure of two lines, one at 583nm and one at 401nm, of the only stable fermionic isotope of atomic erbium as well as determined its isotope shift relative to the four most-abundant bosonic isotopes. Our work focuses on the J->J+1 laser cooling transitions from the [Xe] 4f12 6s2 (3H6) ground state to two levels of the excited [Xe] 4f12 6s6p configuration, which are of major interest for experiments on quantum degenerate dipolar Fermi gases. From a fit to the observed spectra of the strong optical transition at 401nm we find that the magnetic dipole and electric quadrupole hyperfine constants for the excited state are Ae/h=-100.1(3)MHz and Be/h=-3079(30)MHz, respectively. The hyperfine spectrum of the narrow transition at 583nm, was previously observed and accurate Ae and Be coefficients are available. A simulated spectrum based on these coefficients agrees well with our measurements. We have also determined the hyperfine constants using relativistic configuration-interaction ab initio calculations. The agreement between the ab initio and fitted data for the ground state is better than 0.1%, while for the two excited states the agreement is 1% and 11% for the Ae and Be constants, respectively.

Spectroscopy on a single trapped ^137Ba^+ ion for nuclear magnetic octupole moment determination

We present precision measurements of the hyperfine intervals in the 5D3/2 manifold of a single trapped Barium ion, 137 Ba+ . Measurements of the hyperfine intervals are made between mF = 0 sublevels over a range of magnetic fields allowing us to interpolate to the zero field values with an accuracy below a few Hz, an improvement on previous measurements by three orders of magnitude. Our results, in conjunction with theoretical calculations, provide a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants. In addition, we obtain the magnetic octupole constant (C) with an accuracy below 0.1 Hz. This gives a subsequent determination of the nuclear magnetic octupole moment, {\Omega}, with an uncertainty of 1% limited almost completely by the accuracy of theoretical calculations. This constitutes the first observation of the octupole moment in 137 Ba+ and the most accurately determined octupole moment to date.

Wigner Crystals ofTh229for Optical Excitation of the Nuclear Isomer

We have produced laser-cooled Wigner crystals of 229Th3+ in a linear Paul trap. The magnetic dipole (A) and electric quadrupole (B) hyperfine constants for four low-lying electronic levels and the relative isotope shifts with respect to 232Th3+ for three low-lying optical transitions are measured. Using the hyperfine B constants in conjunction with prior atomic structure calculations, a new value of the spectroscopic nuclear electric quadrupole moment Q=3.11(16) eb is deduced. These results are a step towards optical excitation of the low-lying isomer level in the 229Th nucleus.

Precise hyperfine structure measurements of La II utilizing the laser and rf double resonance technique

The hyperfine structure of the 5d 6s b1D2 level in La II has been measured utilizing the laser and radio-frequency double resonance (LRDR) technique in a collinear geometry. Magnetic dipole and electric quadrupole hyperfine constants have been extracted and the results have been compared with previous measurements. With the present technique drastically improved accuracy has been obtained.

Comparative studies using coupled-cluster and unitary coupled-cluster methods: nuclear quadrupole moment, hyperfine constants and transition properties of 27Al

The magnetic dipole and electric quadrupole hyperfine constants of Aluminium (27Al) atom are computed using the relativistic coupled cluster (CC) and unitary coupled cluster (UCC) methods. Effects of electron correlations are investigated using different levels of CC approximations and truncation schemes. The ionization potentials, excitation energies, transition probabilities, oscillator strengths and nuclear quadrupole moment are computed to assess the accuracy of these schemes. The nuclear quadrupole moment obtained from the present CC and UCC calculations in the singles and doubles approximations are 142.5 mbarn and 141.5 mbarn, respectively. The discrepancies between our calculated IPs and EEs and their measured values are better than 0.3%. The other one-electron properties reported here are also in excellent agreement with the measurements.

Relativistic coupled cluster method

Relativistic coupled cluster method (CCM) is applied to compute the low lying excited and ion states of strontium and ytterbium atom. The resulting excitation and ionization energies are in excellent agreement with experimental data and with other correlated calculations. The nuclear magnetic dipole hyperfine constants (A) and electric quadrupole hyperfine constants (B) of excited states are also evaluated and are in accord with experiment. We further address the basis set dependency of the computed properties.

Multiconfiguration Dirac–Hartree–Fock calculations of the hyperfine structures of radium

The multiconfiguration Dirac–Hartree–Fock model has been employed to calculate the magnetic dipole and electric quadrupole hyperfine constants of the 7s6d 3D1, 7s6d 3D2, 7s6d 3D3 and 7s6d 1D2 states of 22388Ra. This paper complements the previously published hyperfine constants for the 7s7p 1P1 and 7s7p 3P1,2 states, yielding the hyperfine structure data for all levels belonging to the two lowest excited-state configurations, 7s7p and 7s6d, of neutral radium.

Comparative studies of the magnetic dipole and electric quadrupole hyperfine constants for the ground and low lying excited states of 25Mg+

We have employed the relativistic coupled cluster theory to calculate the magnetic dipole and electric quadrupole hyperfine constants for the ground and low lying excited states of singly ionized magnesium. Comparison with experimental and the other theoretical results are done and predictions are also made for a few low lying excited states which could be of interest. We have made comparative studies of the important many body effects contributing to the hyperfine constants for the different states of the ion.

On the energy dependence of the Zeeman and hyperfine parameters in the state of OH and OD

Abstract We report quantum beat studies of the energy dependence of the Zeeman parameters in the A 2 Σ + state of OH and OD, and the nuclear hyperfine parameters of OD( A 2 Σ + ). In contrast to previous work, we find that the sign and magnitude of the anisotropic g-factor gl for υ′=0 is consistent with that expected from Curl’s relationship. However, at higher energies gl changes sign, a result we attribute to interaction with the repulsive 1 4 Π state, which is known to lead to predissociation at higher energies. The magnetic and electric quadrupole hyperfine constants were determined for OD( A 2 Σ + ,υ ′ =0–3) , and the constants for υ′=2,3 are reported here for the first time. The derived values are consistent with previous experimental results and available ab initio calculations.

Rotation dependence of electric quadrupole hyperfine interaction in the ground state of molecular iodine by high-resolution laser spectroscopy

Doppler-free high-resolution spectroscopy is applied to molecular iodine at 532 nm by Nd:YAG lasers. The main hyperfine components as well as the crossover lines are measured for R(56)32-0 and P(54)32-0 transitions by heterodyne beating of two I2-stabilized lasers. The measured hyperfine splittings including both main and crossover lines are fitted to a four-term Hamiltonian, which includes the electric quadrupole, spin–rotation, tensor spin–spin, and scalar spin–spin interactions, with an average deviation of ∼1 kHz. Absolute values of the electric quadrupole hyperfine constants for both the upper and the lower states are obtained. The rotation dependence of the ground-state (v″=0) electric quadrupole constant eQq″ is found to be eQq″(J)=-2452.556(2)-0.000164(5)J(J+1)-0.000000005(2)J2(J+1)2 MHz.

Hyperfine-structure calculations in Xe II

The multiconfiguration Dirac-Fock model is employed to compute the hyperfine interaction constants of the 5p45d 4D7/2, 5p46p 4P5/2, 5p46p 2D5/2 and 5p46p 4D7/2 levels of the xenon ion. The wavefunctions are obtained with the active space expansion method, where configuration state functions of a specific parity and J value are generated by substitutions from the reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the expectation values to be monitored. The calculated electric field gradients are combined with experimentally determined electric quadrupole hyperfine constants in order to extract the nuclear electric quadrupole moment of isotope 131 of Xe, for which the value Q = -0.117(6) barn is found.

Large-scale multiconfigurational Dirac-Fock calculations of the hyperfine-structure constants and determination of the nuclear quadrupole moment of49Ti

The multiconfiguration Dirac-Fock (MCDF) model is employed to compute the hyperfine interaction constants of the ${3d}^{2}4s{ }^{2}{D}_{3/2},$ ${3d}^{2}4s{ }^{2}{D}_{5/2},$ ${3d}^{3}{ }^{2}{G}_{7/2},$ ${3d}^{3}{ }^{2}{G}_{9/2},$ and ${3d}^{3}{ }^{2}{P}_{3/2}$ levels of titanium ion. The wave function expansions are obtained with the active space expansion method, where configuration state functions of a specific parity and J value are generated by substitutions from the reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the expectation values to be achieved. The calculated electric quadrupole hyperfine constants are used to evaluate the nuclear electric quadrupole moment of isotope 49 of titanium, for which the value $Q=0.247(11)\mathrm{b}$ is found.

Multiconfiguration Dirac-Fock calculations of the hyperfine structure constants and determination of the nuclear quadrupole moment of yttrium 90

The multiconfiguration Dirac-Fock model is employed to evaluate the effects of relativity and electron correlation on the hyperfine interaction constants of the ${4d5s}^{2}{}^{2}{D}_{3/2}$ and ${}^{2}{D}_{5/2}$ levels of yttrium. The wave-function expansions are obtained with the active space method, where configuration-state functions of a specific parity and $J$ value are generated by substitutions from the reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the hyperfine interaction constants to be studied. The calculated electric quadrupole hyperfine constants are used to evaluate the nuclear electric quadrupole moment of isotope 90 of yttrium, for which the value $Q=\ensuremath{-}0.125(11)$ b is found.

Nuclear quadrupole moment of scandium

The multiconfiguration Dirac-Fock model is employed to evaluate the effects of relativity and electron correlation on the hyperfine interaction constants of the 3${d}^{2}$ ${}^{3}{F}_{3}$, ${}^{3}{F}_{4}$, ${}^{1}{G}_{4}$, and $3d4p$ ${}^{3}{F}_{4}$ levels of Sc II. The wave function expansions are obtained with the active space method, where configuration state functions of a specific parity and $J$ value are generated by substitutions from the reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the hyperfine interaction constants to be studied. The calculated electric quadrupole hyperfine constants, together with previously computed values for other levels of Sc II, are used to evaluate the nuclear electric quadrupole moment of isotope 45 of scandium, for which the value $Q=\ensuremath{-}0.231(4)$ b is found.